渣浆泵扬程特性曲线绘制条件
    目前所有叶片泵的特性曲线H=f(Q)和N=f(Q)，只能通过试验方法来获得，为此要进行泵的标准试验，还没有公认的计算方法，用来估算很宽流量范围内泵的水力损失。
    根据本篇第三章第三节中所述的确定不同流量时理论扬程Hτ= f(Q)和压水室内水力损失hora=f(Q)的方法，通过计算方法可以绘制渣浆泵在相当宽的流量范围内扬程特性曲线H= f(Q)。为此应该给出:
(1)叶轮转速。
(2)叶轮主要参敷:直径D2,出口宽度b2，叶片出口角风，叶片数z，叶片在叶轮出口处的厚度8.
(3)压水室主要参数：压水室断面宽度B，高度h，计算断面和隔舌断面的形式，压力短管喉部断面面积Pr隔舌安放角4 (参阅图3-3-1)。
二、扬程特性曲线绘制方法
    采用下列方法绘制特性曲线H= f(Q):
1)确定不同流量时理论扬程和Ht=f（Q）的关系图线。为此计算下列一些流量值时包括泵特性曲线工作段的参数：

叶轮出口圆周速度ua=Dxn/60和角速度。=rn/30;
叶轮出口轴面速度cs=Q(nD.b.);

叶轮出口液流排挤系数业,不仅考虑叶片厚度，而且要考虑脱流区的存在[根据公
式(3-2-9)];
    叶片出口角修正量AB为 

根据公式(3-2-15)确定每个流量点的理论扬程。

严格地说，Ht不是泵流量的函数，而是流过叶轮液体流量的函数：Q=Q+q.为了简化计算，可以不考虑泄漏量，因为确定这种条件下HT的误差远小于计算本身的误差。

在必要时，利用下列方法考虑泄漏量q。确定泄漏量q，假定它是泵流量的函效，q=f（Q）=Q(1-1)。式中，为了泵的容积效率，根据本章第三节资料，是针对最佳状态确定的。

因此，开始时先求最佳状态的泄露量ga，然后根据下式计算它在其他状态时的值

考虑泄漏量时，利用下列方法给制H-f(0)关系曲线：绘出曲线Ht=f（Q）的每一个点，沿着水平方向小流量侧移动对应给定工作状态的 q值。

(2) 确定对应最高水力效率的状态。如果最佳参数Qam和Har给出，那么可以根据这些参数计算泵对应最佳工作状态的比转速。
    如果泵的最佳参数没有给出，那么求出流量Q-.此值是计算压水室螺旋(环形)泵体内损失时所必需的。
    为了确定Qmzx，从图线Ht=f(Q)坐标原点绘制射线，根据下列关系式确定射线与流量直线的倾斜率
    这条射线与直线Ht=f(Q)的交点就确定了最高水力效率状态(这种方法的理论报据参同本箱第三章第四节)。由这种方法求出的Qnm值与由一些渣浆泵平衡试验数据所得到的这个流量值对比结果指出，试验和计算值具有很好的一致性(误差为5%以下)。同时，流量试验值通常好于计算值，这可以用压水室计算断面上速度变化规律与Ro.=常数偏差不大来说明。
    (3)对与第一节相同的流量，确定压水室内的损失，它是泵压水室螺旋(环形)泵体内和压力短管内的损失之和。
    根据上面所确定的值，利用本篇第三章第三节(参阅计算例子)所述的方法确定压水室(螺旋泵体)内的损失。
    (4)确定叶轮内的水力损失，因为叶轮内的水力损失在很宽流最范围内近似为常数，只有在很小流量状态才开始增大，所以在绘制扬程特性曲线时，在整个讨论流量范围内采用hx=常数。hx值是根据公式hx-Hr.amr(1一m加)针对最佳状态(Qar) 确定的，根据叶片数z选取叶轮的水力效率(参阅本箱第四章第一节)。
    (5)计算泵过流部分总的水力损失: hu=hx + hurs.因为进口短管内的水力损失不大，这里不予考虑(由于进口处的速度低和吸入短管形式——渐缩式或者圆简式，从水力损失观点看是有利的)。
    (6)求泵的扬程H=H-ha.为了估算所提出方法的精度，就要计算20台泵在很宽流量内的扬程。吸入短管直径在125-70mm之间变化，比转速在70~200范围内变化，过流所面尺寸，压水室形状也在很大范围内变化，叶片数在2~4之间变化。
    在接近或者大于最佳流量时，扬程计算值和试验值近似一致(差值为5%~8%). 在Q≤(0.4~0.5)Qar时，发现扬程值离散度较大，在个别情况下可达到10%~12%。出现这种情况的原因是在确定压水室内的水力损失不够精确，因为在很小流量时，液体从计算断面和隔舌之间的区域已经回流到叶轮内，此外，在很小流量时，严格地说叶轮内的水力损失不是常数，它已开始增大，目前还不能估算叶轮内这种增大的水力损失，因此，对于比转速n=70~200，流量Q=(0.51~1.5)Qamn的渣浆泵，可以推荐上述绘制扬程特性曲线的方法。

    在确定实型泵扬程特性曲线时，采用模型泵特性曲线相似系数换算方法，一般考虑所谓尺寸效应，其理由如下。当泵的尺寸增大时，由于过流部生分流道表面相对租糙减小，可

以观察到水力损失有所降低，即提高了水利效率。这种情况将使实型泵扬程比相似换算得到的扬程有所提高。对不同尺寸(比转速相同和特征系数kh2的流道断面相对尺寸）的相似渣浆泵扬程特性曲线分析表明，实际上没有观察到由于尺寸效应而使扬程提高。这是由于液体在渣浆泵流道——叶轮和压水室内流动时主要损失，不是水力摩擦损失，而是混合损失。大家知道，这种损失与粗糙度无关。因此，在用计算方法绘制渣浆泵扬程特性曲线时，可以不考虑尺寸效应。在泵的尺寸增大时，机械效率提高，起码泵的容积效率提高。渣浆泵厂家

Drawing Conditions of Head Characteristic Curve of Slurry Pump

At present, the characteristic curves H = f (Q) and N = f (Q) of all vane pumps can only be obtained by test method. For this reason, there is no accepted calculation method to estimate the hydraulic loss of pumps in a wide flow range.

According to the method of determining theoretical head H_= f(Q) and hydraulic loss hora=f(Q) in pressurized water chamber at different flow rates described in Section 3 of Chapter III of this paper, the head characteristic curve H= f(Q) of slurry pump in a fairly wide flow range can be drawn by calculation method. To this end, it should be given that:

(1) Speed of impeller.

(2) The impeller is mainly applied to: diameter D2, outlet width b2, blade outlet angular wind, blade number z, blade thickness 8 at the outlet of the impeller.

(3) Main parameters of water chamber: width B, height h of water chamber section, form of calculation section and tongue section, throat section area of pressure short pipe Pr tongue placement angle 4 (see Figure 3-3-1).

2. Drawing Method of Head Characteristic Curve

Characteristic curves H= f (Q) are plotted by the following methods:

1) Determine the relationship between theoretical head and Ht=f(Q) at different flow rates. For this purpose, the following flow values are calculated, including the parameters of the working section of the pump characteristic curve:

The circumferential velocity of impeller outlet UA = Dxn/60 and angular velocity. =rn/30;

The impeller outlet velocity cs=Q(nD.b.);

In the field of liquid flow exclusion coefficient at impeller outlet, not only the thickness of blade but also the existence of the stripping zone should be considered.

Formula (3-2-9)];

The blade outlet angle correction AB is

According to the formula (3-2-15), the theoretical head of each flow point is determined.

Strictly speaking, Ht is not a function of pump flow, but a function of liquid flow through impeller: Q = Q + Q. In order to simplify the calculation, leakage can be ignored, because the error of determining HT under this condition is far less than the error of calculation itself.

If necessary, the following methods are used to consider the leakage Q. Determine the leakage q, assuming that it is the function of pump flow, q = f (Q) = Q (1-1). In order to improve the volumetric efficiency of the pump, according to the information in the third section of this chapter, it is determined for the best state.

Therefore, the leakage GA in the best state is calculated at the beginning, and then its value in other states is calculated according to the following formula.

When considering the leakage, the H-f (0) curve is drawn by the following method: each point of the curve Ht = f (Q) is plotted, and the Q value corresponding to the given working state is moved along the small flow side in the horizontal direction.

(2) Determine the state corresponding to the highest hydraulic efficiency. If the optimum parameters Qam and Har are given, then the specific speed of the pump corresponding to the optimum working state can be calculated according to these parameters.

If the optimum parameters of the pump are not given, then the flow Q-. This value is necessary for calculating the internal loss of the screw (annular) pump in the pressurized water chamber.

In order to determine Qmzx, a ray is drawn from the origin of the graph line Ht=f(Q) coordinate, and the slope of the line between the ray and the flow is determined according to the following relations.

The intersection of the ray and the line Ht=f(Q) determines the state of maximum hydraulic efficiency (the theoretical report of this method is referred to in Section 4 of Chapter 3 of this box). The Qnm value calculated by this method is in good agreement with the flow value obtained from some slurry pump equilibrium test data (the error is less than 5%). At the same time, the flow test value is usually better than the calculated value, which can be explained by the small deviation between the velocity variation law calculated by the pressure chamber and the Ro. = constant.

(3) For the same flow rate as the first section, the loss in the pressure chamber is determined, which is the sum of the loss in the screw (annular) pump body and in the short pressure tube of the pump pressure chamber.

According to the values determined above, the loss in the pressurized water chamber (screw pump body) is determined by using the method described in Section 3 of Chapter III (refer to calculation examples).

(4) Determine the hydraulic loss in the impeller, because the hydraulic loss in the impeller is approximately constant in the widest range of flow, and increases only in the very small flow state. So when drawing the head characteristic curve, HX = constant is used in the whole range of flow discussed. The HX value is determined according to the formula hx-Hr.amr (1-m plus) for the optimal state (Qar), and the hydraulic efficiency of the impeller is selected according to the number of blades Z (see Section 1 of Chapter IV of this box).

(5) Calculate the total hydraulic loss of the flow passage part of the pump: Hu = HX + hurs. Because the hydraulic loss of the inlet short pipe is not too large, it is not considered here (because of the low speed at the inlet and the form of the inhalation short pipe - progressive or circular form, it is advantageous from the viewpoint of hydraulic loss).

(6) Calculate the pump head H = H-ha. In order to estimate the accuracy of the proposed method, it is necessary to calculate the head of 20 pumps in a wide flow rate. The diameter of the suction tube varies from 125 mm to 70 mm, the specific speed varies from 70 to 200, the size of the overflow surface and the shape of the water chamber also varies in a wide range, and the number of blades varies from 2 to 4.

When approaching or exceeding the optimal flow rate, the calculated value of head is approximately the same as the experimental value (the difference is 5%~8%). When Q < 0.4~0.5 Qar, it is found that the dispersion of head value is large, and in some cases it can reach 10%~12%. The reason for this is that the hydraulic loss in the pressurized water chamber is not accurate enough, because when the flow rate is very small, the liquid has flowed back into the impeller from the area between the calculated section and the tongue separator. In addition, when the flow rate is very small, the hydraulic loss in the impeller is not a constant, it has begun to increase, and it is not yet possible. This increased hydraulic loss in impeller is estimated. Therefore, for slurry pumps with specific speed n=70~200 and flow Q=(0.51~1.5)Qamn, the above method of drawing head characteristic curve can be recommended.

When determining the head characteristic curve of a real pump, the method of converting the similarity coefficient of the model pump characteristic curve is adopted. The so-called size effect is generally considered.